Year 6 Maths Position and Direction Study Flashcards

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[h] Year 6 Maths Position and Direction Study Flashcards

[q] Plotting Points in the First Quadrant

Coordinates are the location of a point. They are written as (x, y ) where the x coordinate is the distance along the x axis and the y coordinate is the distance up the y axis.

[a] The point (0,0) is called the origin. Points are marked with a dot or small cross.

[q] Plotting Points in the Four Quadrants

The grid can be extended past the origin into four quadrants to give negative numbers on the axes.

[a] Points are plotted in the same way as for the first quadrant except that the x and y values may be negative. This is called plotting points in four quadrants.

[q] Coordinates on a Line

Knowing the coordinates of points on a line will help you find missing coordinates.

[a] Example
Look at grid A below. Look at the coordinates of the points already plotted: (1,3), (2,3), (3,3), (4,3). You will notice that the y coordinate is always 3. So, if you plot another point on this line, its y coordinate will be 3.
Look at grid B. Look at the coordinates of the points already plotted: (4,2), (4,3), (4,4), (4,5). You will notice that the x coordinate is always 4. So, if you plot another point on this line, its x coordinate will be 4.

[q] Translating Points

You can move points across and up or down a coordinate grid. This is called translation.

[a] When you mark the translated points, you add’ after the letter, for example A’, B’, C’.

Example
If you move point A (–10,8) 20 units right and 7 units up, what will the coordinates of the new point A’ be?

The new point A’ has coordinates (10,15).

[q] Translating Shapes

You can translate whole shapes by moving each point in turn.

[a] Example
Translate triangle A 2 squares right and 3 squares up.

By translating each point of the triangle in turn, you can plot the position of the new triangle A’.

[q] Reflecting Points and Shapes in the x Axis

You can use the axes of a coordinate grid as lines to reflect shapes. This is called reflection.

[a] A shape can be reflected in the x axis.

Example
Reflect triangle A in the x axis to produce a new triangle A’.

The coordinates of the vertices of the reflected triangle A’ are (5,–10), (5,–5), (15,–5).

The original shape and the reflected shape are the same size. The original shape has only changed its position. The vertices of the reflected shape are the same distance from the x axis as the vertices of the original shape – they are just on the other side of the axis.

[q] Reflecting Points and Shapes in the y Axis

A shape can be reflected in the y axis.

[a] The vertices of the reflected shape are the same distance from the y axis as the vertices of the original shape – again, they are just on the other side of the axis.

Example
Reflect triangle A in the y axis to produce a new triangle A’’.

The coordinates of the vertices of the reflected triangle A’’ are (–5,10), (–5,5), (–15,5).

[q] Finding Missing Coordinates

You can find missing coordinates by using your knowledge of shapes.

[a] Example
Shape ABCD is a parallelogram. What are the coordinates of point D?

In a parallelogram the opposite sides are parallel and of equal length. So, line BC equals and is parallel to line AD. To get from point B to point C, you go down 15 and along 5. So to go from point A to point D, you also go down 15 and along 5.
Plot point D at (–5,–10).

[q] Unlabelled Axes

Sometimes the axes are not labelled with numbers and there is no grid. However, it’s still possible to work out the missing coordinates.

[a] Example: ABCD is a square. What are the coordinates of point D?

From your knowledge of the properties of a square and what you know about coordinates in a line, you know that point D will have the same x coordinate as point A and the same y coordinate as point C. So the coordinates of point D are (3,1).

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